Research Abstracts Online
January 2010 - March 2011

PI: Philippe de Forcrand, Adjunct Fellow

Quantum Chromodynamics at Finite Density

According to quantum chromodynamics (QCD), quarks are confined at low temperature and low density. QCD also predicts that confinement is lost under extreme conditions: at high temperature, a plasma of quarks and gluons forms; and at high densities and low temperatures, Cooper pairs of two quarks condense, causing color superconductivity. In addition to these three regimes, other phases are likely to exist.

Experimental programs studying the collisions of heavy ions at high energy are underway worldwide to determine the phase diagram of QCD. There is a "race” between such experiments and numerical first-principle lattice simulations to obtain a reliable characterization of this phase diagram. At non-zero quark density, the numerical simulations have to face the "sign problem”: the integral to sample is over an oscillatory function, and importance sampling fails. Information can only be obtained on small volumes and for small densities. To circumvent this problem, these researchers have been pursuing an approach where the simulations are performed with an imaginary chemical potential mu, where the sign problem is absent. Results are fitted with a truncated Taylor expansion, which can be trivially continued back to real mu. The researchers have uncovered an interesting feature of the imaginary-mu phase diagram, in the case of three degenerate quark species: two special values of the mass give rise to tricritical points. The existence and location of these two points provides a benchmark for effective models. In addition, the tricritical scaling behavior in their vicinity constrains the whole phase diagram. The researchers are now extending the determination of these tricritical points to the case of two degenerate quark species.